Review of symbolic software for Lie symmetry analysis

DOI10.1016/S0895-7177(97)00063-0zbMath0898.34002OpenAlexW2022747044MaRDI QIDQ1368549

Willy Hereman

Publication date: 15 October 1998

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0895-7177(97)00063-0

zbMATH Keywords

group-invariant solutionssymbolic computationsLie symmetry softwareLie symmetry reduction

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) NLS equations (nonlinear Schrödinger equations) (35Q55) Lie groups (22E99) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)

Related Items (40)

Symmetry of stochastic non-variational differential equations ⋮ Symmetry classification of quasi-linear PDE's containing arbitrary functions ⋮ Adjoint symmetry and conservation law of nonlinear diffusion equations with convection and source terms ⋮ A consistent approach to approximate Lie symmetries of differential equations ⋮ Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs ⋮ Differential geometric computations and computer algebra ⋮ Symmetry analysis of differential equations with MATHEMATICA ⋮ Review of symbolic software for Lie symmetry analysis ⋮ Sufficient set of integrability conditions of an orthonomic system ⋮ Solutions to nonlinear partial differential equations from symmetry-enhancing and symmetry-preserving constraints ⋮ Nonlocal Extensions of Similarity Methods ⋮ On a new method for finding generalized equivalence transformations for differential equations involving arbitrary functions ⋮ Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation ⋮ Finding higher symmetries of differential equations using the MAPLE package DESOLVII ⋮ Invariance properties of a general bond-pricing equation ⋮ Symbolic computation and differential equations: Lie symmetries ⋮ ASP: automated symbolic computation of approximate symmetries of differential equations ⋮ Symbolic computation of equivalence transformations and parameter reduction for nonlinear physical models ⋮ An optimal system and group-invariant solutions of the Cox-Ingersoll-Ross pricing equation ⋮ Component-trace identities for Hamiltonian structures ⋮ On the simplification of the form of Lie transformation groups admitted by systems of evolution differential equations ⋮ The symbolic integration of exact PDEs. ⋮ Group analysis of variable coefficient diffusion-convection equations. I: Enhanced group classification ⋮ [SADE a Maple package for the symmetry analysis of differential equations] ⋮ Symbolic computation of local symmetries of nonlinear and linear partial and ordinary differential equations ⋮ Solving a nonlinear PDE that prices real options using utility based pricing methods ⋮ Similarity: Generalizations, applications and open problems ⋮ GeM software package for computation of symmetries and conservation laws of differential equations ⋮ Classification of integrable super-systems using the Sstools environment ⋮ Optimal system of Lie group invariant solutions for the Asian option PDE ⋮ A Lie symmetry analysis and explicit solutions of the two‐dimensional ∞‐Polylaplacian ⋮ Associate symmetries: a novel procedure for finding contact symmetries ⋮ Symmetries and exact solutions of the rotating shallow-water equations ⋮ Homogeneity of integrability conditions for multi-parametric families of polynomial-nonlinear evolution equations. ⋮ Conservation laws for the Black-Scholes equation ⋮ Computer algebra solving of first order ODEs using symmetry methods ⋮ Symmetry structure of multi-dimensional time-fractional partial differential equations ⋮ Symmetry analysis of initial-value problems ⋮ Analysis of a class of potential Korteweg-de Vries-like equations ⋮ Size reduction and partial decoupling of systems of equations.

Uses Software

• Maple
• Mathematica
• REDUCE
• SYMMGRP
• FORMINT
• MACSYMA
• LIEPDE
• CRACKSTAR
• DIMSYM
• ApplySym
• CRACK
• LIE
• SYMMGRP.MAX
• diffgrob2
• LIE
• SPDE

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computer algebra application for determining Lie and Lie-Bäcklund symmetries of differential equations
• Automatically determining symmetries of partial differential equations
• Symbolic computations in applied differential geometry
• Nonclassical symmetry reductions of the Boussinesq equation.
• Efficiently implementing two methods of the geometrical theory of differential equations: An experience in algorithm and software design
• Lie algebra computations
• Software to compute infinitesimal symmetries of exterior differential systems, with applications
• Reducing systems of linear differential equations to a passive form
• A REDUCE program for determining point and contact Lie symmetries of differential equations
• Computer algebra application for classification of integrable non-linear evolution equations
• The Riquier-Janet theory and its application to nonlinear evolution equations
• Automatic determination of dynamical symmetries of ordinary differential equations
• Graded differential geometry in REDUCE: Supersymmetry structures of the modified KdV equation
• REDUCE-procedures for the study of adjoint symmetries of second-order differential equations
• Isogroups of differential equations using algebraic computing
• An algorithm for determining the size of symmetry groups
• Nonclassical symmetry reductions of nonlinear partial differential equations
• The computer calculation of Lie point symmetries of large systems of differential equations
• Review of symbolic software for Lie symmetry analysis
• Examples of the investigation of differential equations with modularized programs
• Symmetry reductions and exact solutions of shallow water wave equations
• Symbolic software for soliton theory
• The computer calculation of graded contractions of Lie algebras and their representations
• Index Concepts for General Systems of Partial Differential Equations
• New similarity reductions of the Boussinesq equation
• Symmetries of Differential Equations: From Sophus Lie to Computer Algebra
• Dimensional reductions and exact solutions of a generalized nonlinear Schrodinger equation
• Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution
• Finding abstract Lie symmetry algebras of differential equations without integrating determining equations
• Geometric Aspects of Reduction of Order
• Group analysis of ordinary differential equations and the invariance principle in mathematical physics (for the 150th anniversary of Sophus Lie)
• On the arbitrariness of the general solution of an involutive partial differential equation
• On a shallow water wave equation
• Algorithms for the Nonclassical Method of Symmetry Reductions
• COMPUTER ALGEBRA, SYMMETRY ANALYSIS AND INTEGRABILITY OF NONLINEAR EVOLUTION EQUATIONS
• Solutions of WDVV Equations in Seiberg-Witten Theory from Root Systems
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• A package for the analytic investigation and exact solution of differential equations
• Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries
• LIE, a PC program for Lie analysis of differential equations

This page was built for publication: Review of symbolic software for Lie symmetry analysis